No visible injuries

The sisters were staying at the Maia resort on Seychelles' main island, Mahe.

The Korkki sisters arrived in the Seychelles on September 15.

Seychelles authorities have contacted US officials, and both nations are treating the investigation as high priority, Toussaint said. He declined to provide further information, citing privacy and ongoing investigations.

Calls to the US consular agency in the Seychelles went unanswered.

'This isn't happening'

Worried relatives in the sisters' native Minnesota are seeking answers.

In Minneapolis, their brother told a newspaper that the family is getting no information on the case. Some family members have traveled to the Seychelles to gather details and bring the sisters' bodies home.

"At this point, the only details we know are the articles flying around online," Chris Korkki told the (Minneapolis) Star Tribune this week. "Two things keep going through my mind: This isn't happening, and we just want answers."

He said his sisters were healthy and adventurous, and loved to "experience life to the fullest." They had been posting photos on social media showing them swimming and having fun while on the vacation.

Anne Korkki moved to Denver last year, and worked for JP Morgan Chase, the brother told CNN affiliate KCNC.